Checking and securing understanding of volume of a cylinder | Maths

Starter quiz

This prism has two congruent regular octagonal faces and ______ congruent rectangular faces.

'eight' ✓
Izzy takes some measurements from a cube. Match each measurement to its correct value.

Area of cross-section

⇔

25 cm² ✓

Length of one side

⇔

5 cm ✓

Perimeter of cross-section

⇔

20 cm ✓

Surface area

⇔

150 cm² ✓

Volume

⇔

125 cm³ ✓
The surface area of this octagonal prism is ______ cm².

'668' ✓
The diagram shows a prism unfolded into its net. The perimeter of the cross-sectional face is 70 cm. Which of these statements are correct?

Dimensions of rectangle in the net: 6 cm by 320 cm

Dimensions of rectangle in the net: 6 cm by 70 cm ✓

Total surface area = (320 + 5 × 70) cm²

Total surface area = (2 × 320 + 70 × 6) cm² ✓

Total surface area = (2 × 320 + 5 × (70 × 6)) cm²
The diagram shows the net of a triangular prism. The depth of the prism is 4 cm. The surface area of the prism that can be formed from this net is ______ cm².

'144' ✓
The cross-section of this prism is an equilateral triangle. The surface area of this triangular prism is ______ cm². Give your answer correct to 3 significant figures.

'207' ✓

Exit quiz

Which of these shapes is a cylinder?
Which of these is the formula for the volume of a cylinder?

$V=2\pi r h$

$V=\pi r h$

$V=2\pi r h + 2\pi r^2$

$V=2\pi r^2 h$

$V=\pi r^2 h$ ✓
Which of these are correct for the volume, $V$ , of this cylinder?

$V=\pi\times 10 \times 8$

$V=\pi\times 10^2 \times 8$ ✓

$V=\pi\times 10 \times 8^2$

$V=\pi\times 100 \times 8$ ✓

$V=800\pi$ ✓
Calculate the volume of this semi-cylinder. Give your answer correct to 3 significant figures.

1884 cm³

1130 cm³

565 cm³ ✓

283 cm³

180 cm³
A cylinder fits perfectly inside a cube. The volume of the cube is 1728 cm³. The volume of the cylinder in terms of π is ______π cm³.

'432' ✓
The volume of this cylinder is 360π cm³ . The radius of the cylinder is ______ cm.

'6' ✓

Worksheet

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Lesson Details

Key learning points

A cylinder is not a prism but has a similar structure.
The formula for the volume of a cylinder can be derived by using the formula for a prism.
This can be used to find the volume of any cylinder.
Unknown lengths can be found when the volume of a cylinder is known.

Common misconception

When questions are in context, the height of the cylinder may be described as the depth or length and this can cause some pupils to struggle if they have learned a formula with a particular word.

Remind pupils that the volume of a 3D shape comes from the area of a cross section multiplied by the height or depth. Discuss which length this would be, using a diagram to support.

Keywords

Cylinder - A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.
Volume - Volume is the amount of space occupied by a closed 3D shape.